We introduce a novel approach for computing both ground and excited states of quantum systems. Our method utilizes a nonlinear variational framework and involves approximating wavefunctions using a linear combination of basis functions. These basis functions are enhanced and optimized through the use of normalizing flows.
To validate the accuracy and efficiency of our approach, we performed calculations on various systems. This included determining numerous vibrational states of the triatomic H$_2$S molecule, as well as ground and excited electronic states of simplified one-electron systems like the hydrogen atom, molecular hydrogen ion, and a single-active-electron approximation of a carbon atom.
Our results showcased significant improvements in energy prediction accuracy and accelerated convergence of the basis set, even with the utilization of normalizing flows that had a small number of parameters. Additionally, our approach can be viewed as optimizing a set of intrinsic coordinates that effectively capture the underlying physics within the given basis set.